Modeling the evolution of hummocky topography on debris-covered glaciers

Debris-covered glaciers develop complex, hummocky topography in their ablation zones. The development of hummocky topography coincides with the formation of supraglacial ponds and ice cliffs. Because the ponds and ice cliffs significantly increase melt rates, there is a need to understand how the hummocky topography evolves to better predict melt from debris-covered glaciers. Supraglacial ponds, and the ice cliffs that form along pond shorelines, develop within topographic depressions in the hummocky topography. Recent work (Strickland et al., 2023) showed that topographic depressions on the debris-covered Ngozumpa Glacier, Nepal, undergo positive feedback growth. The development of depressions is often attributed to contrasts in melt rates caused by contrasts in debris thickness. However, this hypothesis cannot explain positive feedback growth because it ignores the negative feedback caused by hillslope debris transport into the depression. Although not included in current models of surface evolution, meltwater drainage provides a potential mechanism for positive feedback depression growth. To better understand depression growth and the evolution of hummocky topography, we develop a two-dimensional topographic evolution model for debris-covered glaciers. Here, we explore how the emergence of englacial debris, hillslope transport of supraglacial debris, and meltwater drainage influence the development of topographic depressions. We first examine the topography that develops from a heterogeneous debris layer. Then, we add the influence of channel incision on topographic evolution. With these mechanisms included, the model only produces small, transient depressions. However, if we include englacial drainage points—locations where supraglacial meltwater and debris enters the subsurface drainage network— this spurs the growth of large, lasting depressions. These results suggest that englacial drainage is necessary to produce persistent depressions in hummocky topography.